Robust state estimator design for uncertain linear systems using optimization techniques

The estimation of state variables of dynamic systems in noisy environments has been an active research field in recent decades. In this way, Kalman filtering approach may not be robust in the presence of modeling uncertainties. So, several methods have been proposed to design robust estimators for the systems with uncertain parameters. In this paper, an optimized filter is proposed for this problem considering an uncertain discrete-time linear system. After converting the subject to an optimization problem, three algorithms are used for optimizing the state estimator parameters: particle swarm optimization (PSO) algorithm, modified genetic algorithm (MGA) and learning automata (LA). Experimental results show that, in comparison with the standard Kalman filter and some related researches, using the proposed optimization methods results in robust performance in the presence of uncertainties. However, MGA-based estimation method shows better performance in the range of uncertain parameter than other optimization methods.     

基于GE的多响应参数稳健设计优化方法

提出了一种基于遗传进化的多响应参数稳健设计优化方法。对多响应参数稳建设计问题进行了数学描述,建立了以试验样本多响应输出参数的加权平均质量损失最小化为目标的数学优化模型;提出了多响应参数稳健设计的遗传进化优化方法：以密集抽样取代离散化处理,以个体取代试验方案,以变化的种群取代固定的内表,通过遗传进化得到最优设计方案;提出并设计了多响应参数稳健设计的遗传优化算法。通过案例分析验证了该方法的有效性。     

Application of SVR,Taguchi loss function,and the artificial bee colony algorithm to resolve multiresponse parameter design problems: a case study on optimizing the design of a TIR lens

Multiresponse parameter design problems have become increasingly important and have received considerable attention from both researchers and practitioners since there are usually several quality characteristics that must be optimized simultaneously in most modern products/processes. This study applies support vector regression (SVR), Taguchi loss function, and the artificial bee colony (ABC) algorithm to develop a six-staged procedure that resolves these common and complicated parameter design problems. SVR is used to model the mathematical relationship between input control factors and output responses, and the ABC algorithm is used to find the optimal control factor settings by searching the well-constructed SVR models in which the Taguchi loss function is applied to evaluate the overall performance of a product/process. The feasibility and effectiveness of the proposed approach are demonstrated via a case study in which the design of a total internal reflection (TIR) lens is optimized while fabricating an MR16 light-emitting diode lamp. Experimental results indicate that the proposed solution procedure can provide highly robust design parameter settings for TIR lenses that can be directly applied in real manufacturing processes. Comparisons with the Taguchi method reveal that the Taguchi method is an undesirable and inappropriate method for resolving multiple-response parameter design problems, while the ABC algorithm can search the solution spaces in continuous domains modeled via SVR instead of in the limited discrete experiment levels, thus finding a more robust design than that obtained by the traditional analysis of variance. Consequently, the proposed integrated approach in this study can be considered feasible and effective and can be popularized as a useful tool for resolving general multiresponse parameter design problems in the real world.     

An intelligent coordinator design for GCSC and AGC in a two-area hybrid power system

This study addresses the design procedure of an optimized fuzzy fine-tuning (OFFT) approach as an intelligent coordinator for gate controlled series capacitors (GCSC) and automatic generation control (AGC) in hybrid multi-area power system. To do so, a detailed mathematical formulation for the participation of GCSC in tie-line power flow exchange is presented. The proposed OFFT approach is intended for valid adjustment of proportional–integral controller gains in GCSC structure and integral gain of secondary control loop in the AGC structure. Unlike the conventional classic controllers with constant gains that are generally designed for fixed operating conditions, the outlined approach demonstrates robust performance in load disturbances with adapting the gains of classic controllers. The parameters are adjusted in an online manner via the fuzzy logic method in which the sine cosine algorithm subjoined to optimize the fuzzy logic. To prove the scalability of the proposed approach, the design has also been implemented on a hybrid interconnected two-area power system with nonlinearity effect of governor dead band and generation rate constraint. Success of the proposed OFFT approach is established in three scenarios by comparing the dynamic performance of concerned power system with several optimization algorithms including artificial bee colony algorithm, genetic algorithm, improved particle swarm optimization algorithm, ant colony optimization algorithm and sine cosine algorithm.     

Hybrid multi-objective shape design optimization using Taguchi’s method and genetic algorithm

This research is based on a new hybrid approach, which deals with the improvement of shape optimization process. The objective is to contribute to the development of more efficient shape optimization approaches in an integrated optimal topology and shape optimization area with the help of genetic algorithms and robustness issues. An improved genetic algorithm is introduced to solve multi-objective shape design optimization problems. The specific issue of this research is to overcome the limitations caused by larger population of solutions in the pure multi-objective genetic algorithm. The combination of genetic algorithm with robust parameter design through a smaller population of individuals results in a solution that leads to better parameter values for design optimization problems. The effectiveness of the proposed hybrid approach is illustrated and evaluated with test problems taken from literature. It is also shown that the proposed approach can be used as first stage in other multi-objective genetic algorithms to enhance the performance of genetic algorithms. Finally, the shape optimization of a vehicle component is presented to illustrate how the present approach can be applied for solving multi-objective shape design optimization problems.     

A new hybrid artificial bee colony algorithm for robust optimal design and manufacturing

The purpose of this paper is to develop a novel hybrid optimization method (HRABC) based on artificial bee colony algorithm and Taguchi method. The proposed approach is applied to a structural design optimization of a vehicle component and a multi-tool milling optimization problem.A comparison of state-of-the-art optimization techniques for the design and manufacturing optimization problems is presented. The results have demonstrated the superiority of the HRABC over the other techniques like differential evolution algorithm, harmony search algorithm, particle swarm optimization algorithm, artificial immune algorithm, ant colony algorithm, hybrid robust genetic algorithm, scatter search algorithm, genetic algorithm in terms of convergence speed and efficiency by measuring the number of function evaluations required.     

A new design optimization framework based on immune algorithm and Taguchi's method

This paper describes an innovative optimization approach that offers significant improvements in performance over existing methods to solve shape optimization problems. The new approach is based on two-stages which are (1) Taguchi's robust design approach to find appropriate interval levels of design parameters (2) Immune algorithm to generate optimal solutions using refined intervals from the previous stage. A benchmark test problem is first used to illustrate the effectiveness and efficiency of the approach. Finally, it is applied to the shape design optimization of a vehicle component to illustrate how the present approach can be applied for solving shape design optimization problems. The results show that the proposed approach not only can find optimal but also can obtain both better and more robust results than the existing algorithm reported recently in the literature.     

An ellipsoid algorithm for probabilistic robust controller design

In this paper, a new iterative approach to probabilistic robust controller design is presented, which is applicable to any robust controller/filter design problem that can be represented as an LMI feasibility problem. Recently, a probabilistic Subgradient Iteration algorithm was proposed for solving LMIs. It transforms the initial feasibility problem to an equivalent convex optimization problem, which is subsequently solved by means of an iterative algorithm. While this algorithm always converges to a feasible solution in a finite number of iterations, it requires that the radius of a non-empty ball contained into the solution set is known a priori. This rather restrictive assumption is released in this paper, while retaining the convergence property. Given an initial ellipsoid that contains the solution set, the approach proposed here iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the solution set. At each iteration a random uncertainty sample is generated with a specified probability density, which parameterizes an LMI. For this LMI the next minimum-volume ellipsoid that contains the solution set is computed. An upper bound on the maximum number of possible correction steps, that can be performed by the algorithm before finding a feasible solution, is derived. A method for finding an initial ellipsoid containing the solution set, which is necessary for initialization of the optimization, is also given. The proposed approach is illustrated on a real-life diesel actuator benchmark model with real parametric uncertainty, for which a robust state-feedback controller is designed.     

混合自适应遗传算法优化多目标染色配方模型

从提高染色产品质量和效益的角度出发,综合考虑如染料浓度、温度、时间和助剂浓度等因素影响,构建了多目标染色工艺配方优化模型。针对传统遗传算法普遍存在的问题和缺陷,提出基于正交试验设计、自适应交叉操作及局部搜索等技术进行算法改进,并利用改进后的算法获得配方模型最优解的解决方法:。实践结果:证明,混合自适应遗传算法使种群更具有代表性和全面性,最大程度的继承了父代的优良特性,改善了算法的早熟现象并增强其寻优性能。最终以较少的计算量和较高的收敛速度对全局进行快速的搜索,比传统遗传算法得到的优化目标值降低了l0.8%左右。该方法:可推广应用于其他复杂过程的优化求解问题中。     

膜系统下的一种多目标优化算法

提出一种基于膜优化理论的多目标优化算法,该算法受膜计算的启发,结合膜结构、多重集和反应规则来求解多目标优化问题。为了增强算法的适应能力,采用了遗传算法中的交叉与变异机制,同时在膜中引入外部档案集,并采用非支配排序和拥挤距离方法对外部档案集进行更新操作来提高搜索解的多样性。仿真实验采用标准的KUR和ZDT系列多目标问题对所提出的算法进行测试,通过该算法得出的非支配解集能够较好地逼近真实的Pareto前沿,说明所提算法在求解多目标优化问题上具有可行性和有效性。     

Neuro-genetic approach to optimize parameter design of dynamic multiresponse experiments

Engineers have widely applied the Taguchi method, a traditional approach for robust experimental design, to a variety of quality engineering problems for enhancing system robustness. However, the Taguchi method is unable to deal with dynamic multiresponse owing to increasing complexity of the product or design process. Although several alternative approaches have been presented to resolve this problem, they cannot effectively treat situations in which the control factors have continuous values. This study incorporates desirability functions into a hybrid neural network/genetic algorithm approach to optimize the parameter design of dynamic multiresponse with continuous values of parameters. The objective is to find the optimal combination of control factors to simultaneously maximize robustness of each response. The proposed approach is based on three stages which (1) use neural networks for constructing a response function model of a dynamic multiresponse system, (2) use exponential desirability functions for evaluating overall performance of a specific factor combination, and (3) use a genetic algorithm to optimize parameter design. Effectiveness of the proposed approach is illustrated with a simulated example. Analysis results reveal that the approach has higher performance than the traditional experimental design.     

μ/km-design with time-domain constraints

Standard μ/k_m-synthesis approaches cannot handle specifications on closed-loop time responses in a direct manner. On the other hand, constrained H_∞ optimization handles explicitly time-domain specifications in an H_∞-optimal control setting but is conservative with respect to structured model uncertainty. In this paper, the authors propose a constrained μ/k_m-synthesis approach to design robust controllers for uncertain systems with time-domain constraints and structured real/complex model uncertainties. They derive an algorithm based on an iteration process involving a search for multipliers and the solution of scaled constrained H_∞-optimization problems     

MRCD: a genetic algorithm for multiobjective robust control design

A genetic algorithm (GA) for the class of multiobjective optimization problems that appears in the design of robust controllers is presented in this paper. The design of a robust controller is a trade-off problem among competitive objectives such as disturbance rejection, reference tracking, stability against unmodeled dynamics, moderate control effort and so on. However, general methodologies for solving this class of design problems are not easily encountered in the literature because of the complexity of the resultant multiobjective problems. In this paper, a recently developed class of GAs, multiobjective GAs, are used to solve robust control design problems. Here, a new algorithm, called multiobjective robust control design, has been proposed. The structure and operators of this algorithm have been specifically developed for control design problems. The performace of the algorithm is evaluated by solving several test cases and is also compared to the standard algorithms used for the multiobjective design of robust controllers.     

Particle swarm optimization-based fixed-structure <Emphasis Type="Italic">ℋ</Emphasis><Subscript>∞</Subscript> control design

In this paper, a new robust fixed-structure ℋ _∞ controller design based on the Particle Swarm Optimization (PSO) technique is proposed. The optimization-based structured synthesis problem is formulated and solved by a constrained PSO algorithm. In the proposed approach, the ℋ _∞ controller’s structure is selectable. PI and PID controller structures are especially adopted. The case study of an electrical DC drive benchmark is adopted to illustrate the efficiency and viability of the proposed control approach. A comparison to another similar evolutionary algorithm, such as Genetic Algorithm Optimization (GAO), shows the superiority of the PSO-based method to solve the formulated optimization problem. Simulations and experimental results show the advantages of simple structure, lower order and robustness of the proposed controller.     

Hybrid Taguchi-genetic algorithm for global numerical optimization

In this paper, a hybrid Taguchi-genetic algorithm (HTGA) is proposed to solve global numerical optimization problems with continuous variables. The HTGA combines the traditional genetic algorithm (TGA), which has a powerful global exploration capability, with the Taguchi method, which can exploit the optimum offspring. The Taguchi method is inserted between crossover and mutation operations of a TGA. Then, the systematic reasoning ability of the Taguchi method is incorporated in the crossover operations to select the better genes to achieve crossover, and consequently, enhance the genetic algorithm. Therefore, the HTGA can be more robust, statistically sound, and quickly convergent. The proposed HTGA is effectively applied to solve 15 benchmark problems of global optimization with 30 or 100 dimensions and very large numbers of local minima. The computational experiments show that the proposed HTGA not only can find optimal or close-to-optimal solutions but also can obtain both better and more robust results than the existing algorithm reported recently in the literature.     

基于复杂昂贵仿真的体系效能多目标优化

效能优化是实现体系结构设计、多方案配置等工作的重要途径.体系仿真系统通常具有组成结构复杂、连续离散混合、输入输出变量多、运行开销大等特点,导致效能优化面临多目标、混合变量、多峰值、低效率等问题,提出一种基于复杂昂贵仿真的体系效能优化算法.针对昂贵仿真问题,提出基于聚类与空间填充准则相结合的开发-探索序贯元模型策略;引入...     

Quantum inspired evolutionary algorithm for ordering problems

This paper proposes a new quantum-inspired evolutionary algorithm for solving ordering problems. Quantum-inspired evolutionary algorithms based on binary and real representations have been previously developed to solve combinatorial and numerical optimization problems, providing better results than classical genetic algorithms with less computational effort. However, for ordering problems, order-based genetic algorithms are more suitable than those with binary and real representations. This is because specialized crossover and mutation processes are employed to always generate feasible solutions. Therefore, this work proposes a new quantum-inspired evolutionary algorithm especially devised for ordering problems (QIEA-O). Two versions of the algorithm have been proposed. The so-called pure version generates solutions by using the proposed procedure alone. The hybrid approach, on the other hand, combines the pure version with a traditional order-based genetic algorithm. The proposed quantum-inspired order-based evolutionary algorithms have been evaluated for two well-known benchmark applications – the traveling salesman problem (TSP) and the vehicle routing problem (VRP) – as well as in a real problem of line scheduling. Numerical results were obtained for ten cases (7 VRP and 3 TSP) with sizes ranging from 33 to 101 stops and 1 to 10 vehicles, where the proposed quantum-inspired order-based genetic algorithm has outperformed a traditional order-based genetic algorithm in most experiments.     

An efficient metamodel-based multi-objective multidisciplinary design optimization framework

This paper presents an efficient metamodel-based multi-objective multidisciplinary design optimization (MDO) architecture for solving multi-objective high fidelity MDO problems. One of the important features of the proposed method is the development of an efficient surrogate model-based multi-objective particle swarm optimization (EMOPSO) algorithm, which is integrated with a computationally efficient metamodel-based MDO architecture. The proposed EMOPSO algorithm is based on sorted Pareto front crowding distance, utilizing star topology. In addition, a constraint-handling mechanism in non-domination appointment and fuzzy logic is also introduced to overcome feasibility complexity and rapid identification of optimum design point on the Pareto front. The proposed algorithm is implemented on a metamodel-based collaborative optimization architecture. The proposed method is evaluated and compared with existing multi-objective optimization algorithms such as multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGA-II), using a number of well-known benchmark problems. One of the important results observed is that the proposed EMOPSO algorithm provides high diversity with fast convergence speed as compared to other algorithms. The proposed method is also applied to a multi-objective collaborative optimization of unmanned aerial vehicle wing based on high fidelity models involving structures and aerodynamics disciplines. The results obtained show that the proposed method provides an effective way of solving multi-objective multidisciplinary design optimization problem using high fidelity models.     

Robust topology optimization accounting for misplacement of material

The use of topology optimization for structural design often leads to slender structures. Slender structures are sensitive to geometric imperfections such as the misplacement or misalignment of material. The present paper therefore proposes a robust approach to topology optimization taking into account this type of geometric imperfections. A density filter based approach is followed, and translations of material are obtained by adding a small perturbation to the center of the filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued random field. The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined as a weighted sum of the mean value and the standard deviation of the performance of the structure under uncertainty. A sampling method is used to estimate these statistics during the optimization process. The proposed method is successfully applied to three example problems: the minimum compliance design of a slender column-like structure and a cantilever beam and a compliant mechanism design. An extensive Monte Carlo simulation is used to show that the obtained topologies are more robust with respect to geometric imperfections.